Сборник задач ТСПП

5. . .

( , , .) –

,’ (. 5.1), ,

; .

F		!		"
		.		,
		F
–	#–		.

$ . 5.1

%

F =0 =F- F=

–F. F

&

F> 0– (,# “

”) – ,

F< 0 – .' ,

Fo= n

–

i

,

.

5.1.

(. 5.1),

F3-4 = 1,0

F1-2= –,2

F1 = 4.

5.1.

=2 2 ;F 2 ;F= 2+

10=

12

:F2= 4−

3

4

F1 4=

1F+2

3F= 410− =2 8,

:

−

−

−

F1− 4=

4F− =1F12−

=4 .

5.2.

!

mc = ,10

D = 3

, " # " (

= 30˚,

)

= /6, L=

120,!0

"

w

= 0,01w = ,0,5.

5.2.

( ) (. 5.2):

F′ =

F′ +

F′ , F′TC

F′TK –

.

T

TC

TK

cosβ +

β sin=

) 1000

9,81+ = (0,

F′

m

g

=

(ω

TC

c

ω

c

β

+

β

=

+

=

′

= ρ

FTK

L

(g

cos

sin

) 1200 6 9,81(0

F′ = 49903+

66041=

T

51

$	:*′ =	F′T R=	115944= 1,5.173916
( ):′T′ =		′′TC+ ′	=T	49903 ′ =
	F	F '	F	F%'
$	:*′′ =	F′′T R=	49903= 1,5.7485

% . 5.2

5.25.3

5.#3.

5.2

mc = .4

5.3.

: (

):

w

.

F′

=

m

g

)

4000−

9,81=

(0,

(sinβ −

β cos=

ÃÐC

c

c

:

L g

w=

F′′

=

′ F ′′

F

′ F

β

+

=

+

ρ

(sinβ −

ê

ÃÐC

ÃÐC

ÃÐÊ

ÃÐÑ

ê

=

19279+

6

1200−9,81

(0,5= 0,5 0,87) 19747

& :Ì′′ÒÐ= ′′ FÃÐC

= R19747á =

1,5

5.4.

*'$ = *0

,

, 5.25.'3 " :

, .( !

" " 5.,52.35.4

'5.4. :

– :*′0= 96665= 1,5 144997;

– :*′′0= 63411= 1,5 95116;

52

– :*′′′0= 30156= 1,5 45234.

) , " "

, ( 5.25.3) – ,

.

. 5.3 ! .

% . 5.3 5.4

5.#5. 5.,52.35.4 , # " "

( )! # w = 0,14* .

" ! ,

" .

		5.6.
,
				"(	" ) : . =				. = 8000
							F	F
#											3 .
		(5.6.									F = 3 · 800,0 =
						F = 24000 + 800.0 = 32000
		5.$7.
F	=			1000, 0
F	= 200.0								,
,
										1:4.
										8000 = 200. 0
		)5#.7.			:F				= ,F
1200.)0									P= 4000 ·.2 =
		5.8+. "
"										# " ,
# ,									10,
				– 80?, !0			"			w = 0,01.

53

, ’ (

), #

# .
+ (		, )
	–		, , .
# , #

.+

,# , .+

, , (, )

# .! ,# , (		)
	– ,
	( ).
, , ,
# ,
– ,

.- , ( , ,

),

.

% , ’

, ( ,#

,

).

. #

( , , )

– / .0 :

(

)

#

#

:

F

F

fα

F=

"–

F ;α

–

, .

$ , , (

)

’

: (

–

α

), #

# α

–

,

#

;

(

, –

α

)#

,

# α #

α .0 α .

1 ,α α=+α	; α	α=

α .

54

α " / - .% ,

, / :

	fα				fα
F=		,		F=		.
F				F
+

#

, ,				–				.
, (				)								( )
(	) :$ .max= Pψ , $											–
# ,			(			) ,ψ			"–
,			$–max=				,			maxM –
						M
						ma
, R – .
5.$9. " "
		(. 5."4)								"
5 .		( )

# , ,

"
F	50.0

% . 5".4. ( 5.9)

5.9.			:
F=	F+	=F − F ;		F=	, F=
o	ò	ê	íá		íá
" :
F=	F−	;Fc= 5− 0,5= 4,
ò	o

'

) " .

F= +F= 50F ,

o ò ê

(

5.10. ( )

(. 5.5) ,

"		, β = 3 ; w= 0 ;
w= 0 ;ρ = ;z=	;m= 3000;m = 1000;L=		ê
			8 ;v= ;
ñ
k= 0 ;Θ = 1 .( !		, .
ø

55

)

)

% . 5".5. " ( 5.10)

5.10. #

F.

=

+ ρ

β +

+ ρ

m

β =

L g

( z

mc

w

)L wcosg (

z

= (3 3000+ 0,01

5 800+0,5)+9,81

0,871 0,5= (383000. 5 800

$

(

)

F = z m(gcosβw+ β sin=

) 3

3000

9,81+ = (0, .

íá. ê³í

áð

c

% . 5.6 5.10

F = z m (singβ −				βwcos= )		3 1000− 9,81= (0, .
çá. ïî÷	òàðè			c
$
F = F+ ρ	L(singβ −			βwcos=	+)	14458 5− 800 9,81=	.
çá. ê³í . çá ïî÷				c
- "	t=	L=	800= 21 .
		v k4 0,95
	ø			200= .
- % = t+ Θ = 211+

56

. !							F	!
			o=	−	( . 5.6).
			F F
5.11) . "
"		"		( .		5*.7).		– 2,
(						)		20	m( = 200; 0
m	=	1200				=	0,01;
			),w =			0,2w ;	" "
# 3,5;! " "									w#	=w,
					– 4/.			,#
;										G	–
5000.
										"
		" # .

% . "5.7 ( 5.11)

5.12) .		4.3	G
" # ,
" , ! #
	( I f–= 0,1f;=II0,15– f;=II0,2)+I –.
, # "			"
	( 1) ? ,
- .
5.13). 5.#11 :)
" β =		L= 10 ; )	" " .

( " "

# .

5.14.

2000.+0 "

(F) F() , f= 0 , α = 2 ?+

, f0,2;0,3= α =;10,6? ,

5.15. α = 2 ,f= 0

Fo= 15000

.+ " ,

57

10%# ?(	!	(
) Fo(α #	.

5.16*. #

. ,

, # # ( , "

- , )/?

" ?

5.17$ .

'			., "
	–	180˚!,	(	) " "
		f= 0 . :

( ) " " ,

F= 15000, " ;

,

180˚.

5.18+.# !

" 5.,17

:) ; )# – 2 # ; ) – 2 # # .

5.19$ .

., "

– 240˚!, ( ) f= 0 .

"

" , F= 10000, . ,

" "
" " .
5.20.
, F=		15000,		1/4,			,		f= 0	.
			=		α = 2
			F
5.21+.
,										,
,"								,
F= 10000,α = 2 ,f= 0 ,			=	5 ?
			F

58

5.22,.	5.21	" , ,
F= 20000,	F= − 5000.

,

.

5.23.				"
		140 ( ), !
	ψ = 0 ,ψ = 0 ,ψ = 0 .+
( ),
( " )			2,8?

5.24) . 5.23 ,

" (

), ! "

f= 0 .

5.25+.

' ,

" " " =1 +2 = 200˚ + 200˚

! f= 0,3,

G = 50000
, "	F1 2= 15000?+
	−

?

% . 5.8

5.25

'5.25. " " .

f(α 1+α 1 )

8 .0

F1 2= 15000, F2=

/

F=

=

G= 50000= 25000,

F

−

2 2

F1= F=

=

.$

F=

F8,14=

−

8 .

25000 1500

0 , o= −

=

81400− = 10000, 71400

F F F

F= 81400−

25000= .56400

−

3 4*

, " f

" "

α

α

#

F1=

f1 =

f2 ,

2≈ 18000,

1≈ 63000.

F

F

2

F

59

5.26.		,
	-				N(1 =N2),
	" = 420˚",			# 1 = 200˚
!			f = 0,3. #
"		.+

N1 =N2?2

5.27(. (

) : , = 210˚f= ,0,5

- ,1 = 180˚,2 = 180˚f= ,0,2N1 =,N2.0

.

5.28. 2"0 " m( = 120)0

8"	#
# 3/.(	# "

800, " ip 10‰= . "

, ! " 2 = 0,07. ,

# " # # 1/,

! " w = 0,015.

5.29. ,

" "( " ),

: " ! " ; "

! " .

5.30/ .					110
:# – 1,0				20,		–
40, . ,
2						= 0,2
:)					; )
( ’			) .
5.31* ".	14

, .

" , , #

2 = 0,15, S = 1,2 d = 80.0

60